Best Known (220−22, 220, s)-Nets in Base 2
(220−22, 220, 95325)-Net over F2 — Constructive and digital
Digital (198, 220, 95325)-net over F2, using
- net defined by OOA [i] based on linear OOA(2220, 95325, F2, 22, 22) (dual of [(95325, 22), 2096930, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2220, 1048575, F2, 22) (dual of [1048575, 1048355, 23]-code), using
- 1 times truncation [i] based on linear OA(2221, 1048576, F2, 23) (dual of [1048576, 1048355, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 1 times truncation [i] based on linear OA(2221, 1048576, F2, 23) (dual of [1048576, 1048355, 24]-code), using
- OA 11-folding and stacking [i] based on linear OA(2220, 1048575, F2, 22) (dual of [1048575, 1048355, 23]-code), using
(220−22, 220, 149796)-Net over F2 — Digital
Digital (198, 220, 149796)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2220, 149796, F2, 7, 22) (dual of [(149796, 7), 1048352, 23]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2220, 1048572, F2, 22) (dual of [1048572, 1048352, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2220, 1048575, F2, 22) (dual of [1048575, 1048355, 23]-code), using
- 1 times truncation [i] based on linear OA(2221, 1048576, F2, 23) (dual of [1048576, 1048355, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 1 times truncation [i] based on linear OA(2221, 1048576, F2, 23) (dual of [1048576, 1048355, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2220, 1048575, F2, 22) (dual of [1048575, 1048355, 23]-code), using
- OOA 7-folding [i] based on linear OA(2220, 1048572, F2, 22) (dual of [1048572, 1048352, 23]-code), using
(220−22, 220, 5147693)-Net in Base 2 — Upper bound on s
There is no (198, 220, 5147694)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 684996 801490 468872 881472 235307 528309 929610 918223 519471 704017 740550 > 2220 [i]